高考数学一轮复习练?解三角形及其综合应用 - 百度文库

5.4 μۺӦ

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һ ҶҶ

1.ڡABC,A,B,CĶԱ߷ֱΪa,b,c,sin A=3sin B,c=5,cos C=5

6,a=( ) A.22 B.3 C.32 D.4 B

2.ABCڽA,B,CԵı߷ֱΪa,b,c,֪bsin 2A=asin B,c=2b,????

( ) A.34

2 B.3 C.2 D.3 D

3.ڡABC,ڽA,B,CĶԱ߷ֱΪa,b,c,b2

+c2

-3bc=a2

,bc=3a2

,CĴС( A.л2 B. C.2 D.63336

A

4.ABCΪ3(a2

+c2

-b2

),ҡCΪ۽,B= ;??4

??

ȡֵΧ .

3

;(2,+)

5.ڡABC,a,b,cֱΪڽA,B,CĶԱ,2asin A=(2b+c)sin B+(2c+b)sin C. (1)AĴС;

(2)sin B+sin C=1,жϡABC״. (1)֪,Ҷ, 2a2

=(2b+c)b+(2c+b)c,a2

=b2

+c2

+bc.

a2

=b2

+c2

-2bccos A,

bc=-2bccos A,cos A=-12

. AΪεڽ,A=23

. (2)֪2asin A=(2b+c)sin B+(2c+b)sin C, Ҷ,

2sin2

A=(2sin B+sin C)sin B+(2sin C+sin B)sin C,

sin2

A=sin2

B+sin2

C+sin Bsin C=sin

22

=334

. sin B+sin C=1,

sin2

B+sin2

C+2sin Bsin C=1,

sin B=sin C=12

,

Ϊ0

1

)

B=C=, ԡABCǵ.

6

μۺӦ

6.ڡABC,ֱ߳Ϊa,a+2,a+4,СǵֵΪ,εΪ( )

153 4

1314

A.

B. C.

154213 4

D.

353 4

A

7.ͼʾ,Ϊ˲A,Bľ,СDΪ۲,A,BֱDıƫ30㡢ƫ30㷽,ʻ40ﵽC,BC,ACıƫ60㷽,A,BľΪ( )

A.203 B.403 C.20(1+3) D.40 B

8.ǡABCڽA,B,CĶԱ߷ֱΪa,b,c,c=1,A=2C,ABCܳȡֵΧΪ( ) A.(0,2+2) B.(0,3+3) C.(2+2,3+3) D.(2+2,3+3] C

9.ͼ,һһˮƽĹ·ʻ,Aʱù·һɽDƫ30ķ,ʻ600 m󵽴B,ôɽƫ75ķ,Ϊ30,ɽĸ߶CD= m.

1006

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һ Ҷ

1.(2019У,10)ABCڽA,B,CĶԱ߷ֱΪa,b,c,A. B. C. D. B

2.(2020츣֥ѧѧϰЧ,7)ABCڽA,B,CĶԱ߷ֱΪa,b,c,ABCC=( )

2

??2+??2-??2

Ϊ,

4

6

3

23

56

sin????

+=1,

sin??+sin????+??

C=( )

A. B. C. D. C

3.(2019Ϻɽģ,7)֪ABC,tan A=,tan B=,AB=17.:

45(1)CĴС;

(2)ABC̱ߵı߳.

+tan??+tan??

(1)tan C=tan[-(A+B)]=-tan(A+B)=-=-4153=-1,

1-tan??tan??1-

4513

2346

13

C=.

(2)Ϊtan A

????????

=, sin??sin??

????sin??1717BC==2sin??

21734

14

1717

.

=2.

ʡABC̱ߵı߳Ϊ2.

״ж

4.(2020ɽ10¿,8)ڡABC,sin A=2sin Bcos C,a=b+c-bc,ABC״( ) A.ȱ B. C.ֱ D.ֱ A

5.(2018ʦ12¿,6)ڡABC,ڽA,B,CĶԱ߷ֱa,b,c,A. B.ֱ

C.۽ D.λֱ D

6.(2018ϳһ,6)ڡABC,ڽA,B,CĶԱ߷ֱΪa,b,c,A.90ڽ B.60ڽ C.45ڽ D.30ڽ B

tan??-tan????-??

=,αغ(

tan??+tan????

??cos??1+cos2??

=,ABC??cos??1+cos2??

2

2

2

״( )

)

εΧйص

7.(2020ɹźܶѧһ¿,18)ڡABC,A=60,c=a. (1)sin Cֵ; (2)a=7,ABC.

(1)ڡABC,ΪA=60,c=a,Ҷsin C=(2)Ϊa=7,c=7=3.

Ҷa=b+c-2cbcos A7=b+3-2b3,b=8b=-5().ԡABCS=bcsin A=83=63. 22222

2

2

2

2

2

3

7

37??sin??3333==. ??7214

3

7

1113 3

8.(2019ٴһ12¿,17)ڡABC,A,B,CĶԱ߷ֱa,b,c,2csin B=3atan A. (1)

??+??2

ֵ; ??22

(2)a=2,ABCֵ.

(1)2csin B=3atan A?2csin Bcos A=3asin A?2bccos A=3a,

2

2bc

??+??2-??22222

=3a,b+c=4a, 2????

2

??2+??2

=4. ??22

2

(2)a=2,b+c=16,cos A=b+c2bc,8bc,

2

2

??2+??2-??26

=. 2????????

ҽb=cʱ,ȡȺ, cos A=. cos A=bc=A(0,),

SABC=bcsin A=3tan A. 2

63

84

6????6

, cos??

2

12

1+tanA=1+tan A=

sin2Acos2A+sin2A1

==2, 22cosAcosAcosA

1167-1ܡ-1=, cos2A93

SABC=3tan Aܡ7,

ʡABCֵΪ7.

εʵӦ

9.(2018¿,8)AD,ACΪ45,BDƫ60㴦,CBĸΪ30,AB84,Ϊ( ) A.24 B.125 C.127 D.36 C

10.(2018ӱʯׯ׿,17)ijѧУƽʾͼͼеABCDE,ABEΪ,ıBCDEΪѧ,AB,BC,CD,DE,EA,BEΪѧУҪ·(ǿ).BCD=CDE=,BAE=,DE=3BC=3CD= km. (1)·BEij;

(2)ABEֵ.

2

3

3

910

(1)ͼ,BD,ڡBCD,BD=BC+CD-2BCCDcosBCD=

2

2

2

2733,BD=(km). 10010 4

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